To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation o...To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.展开更多
基金This work was supported by the National Natural Science Foundation of China under Grants No. 61103191, No. 61070215 the Funds of Key Lab of Fujian Province University Network Security and Cryptology under Crant No. 2011003 and the Open Research Fund of State Key Laboratory of Inforrmtion Security.
文摘To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.
